## Why
Realtime connections construct API providers directly, bypassing the residency override applied by higher-level model provider code. Configured provider headers could therefore take precedence over managed residency requirements.
## What changed
Apply the shared process-wide residency requirement in `ModelProviderInfo::to_api_provider`. With `enforce_residency = "us"`, the managed value overrides both static and environment-supplied residency headers, including for realtime WebSocket connections and WebRTC calls and sideband connections. Preserve unrelated headers and configured residency values when no managed requirement is set.
Share the residency policy with default HTTP headers, remove redundant enforcement at callers, and recover the stored policy from poisoned locks.
## Testing
Add a provider unit test for managed and unmanaged header behavior without mutating provider configuration. Add realtime integration coverage across WebSocket and WebRTC transports, managed and unmanaged residency, and static and environment-supplied headers.
GitOrigin-RevId: 98ceb456cc97f88241df5a829c72288aa5e66aec
bee042d119